Convergence of the costates does not imply convergence of the control
Abstract
Solving an optimal control problem using a digital computer
implies discrete approximations. Since the 1960s, there have
been well-documented [1–3] naïve applications of Pontryagin’s
principle in the discrete domain. Although its incorrect applications
continue to this day, the origin of the naïvete is quite understandable
because one has a reasonable expectation of the validity of
Pontryagin’s principle within a discrete domain. That an application
of the Hamiltonian minimization condition is not necessarily valid in
a discrete domain [1,4] opens up a vast array of questions in theory
and computation [2,5]. These questions continue to dominate the
meaning and validity of discrete approximations and computational
solutions to optimal control problems [6–10]. Among these
questions is the convergence of discrete approximations in optimal
control.
Description
The article of record as published may be found at http://dx.doi.org/10.2514/1.37331
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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